The parens are being interpreted as special chars inside the regex. Use the quotemeta operator to escape them, and they'll retain their literal meaning.

$line =~ s/\Q$var//;
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As in:

#!/usr/bin/perl -wT
use strict;

my $var = 'apple (banana) cherry';
my $line = 'apple (banana) cherry kiwi lemon melon';
$line =~ s/\Q$var//;

print "$line\n";

=output
 kiwi lemon melon
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-Blake